Bachelor/Master Seminar:
Optimization (Flow Matching and Inverse Problems)
WS 2026/27
| Lecturer: |
Prof. Dr. Steffen Dereich Prof. Dr. Benedikt Wirth |
Information on the seminar
| Time, location: |
tba |
| Learnweb: | please sign up in https://sso.uni-muenster.de/LearnWeb/learnweb2/course/view.php?id=95229 |
| Content: | This seminar explores the theoretical and algorithmic foundations of "Flow Matching", a highly active paradigm in generative Artificial Intelligence. Instead of modeling probability densities directly, these methods learn time-dependent vector fields that continuously transport a simple base distribution into a complex data distribution. We will treat Flow Matching not merely as a single algorithm, but as a flexible toolkit comprising probability paths, stochastic processes, and measure couplings. A central focus of the seminar is the underlying connection to Optimal Transport (OT) theory, including conditional Wasserstein distances and minibatch couplings. Furthermore, we will highlight practical applications in computer vision and image processing. In particular, we will discuss how pre-trained generative models can be utilized as "plug-and-play" priors for solving inverse problems, bridging the gap between classical image restoration and Bayesian inference. The goal of this seminar is to understand both the unifying mathematical frameworks and the state-of-the-art algorithmic developments in this dynamic research area. |
| Prerequisites: | Analysis I-III; a specialization in a module on one of the fields numerics, analysis, stochastics will be helpful. |
| assessment: | 90-minute seminar talk and written report (ca. 7-page handout, to be presented and discussed with the lecturer ca. 10 days before the talk, to allow for improvements and further assistance) |
| Participation: | If you are interested, please contact us by e-mail. |
| Topics: |
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